You are working for a power plant that is located on ahighway that runs east to west. The town of Cortez islocated 49 miles east of the power plant, and 6 miles northof the freeway. The town of Joplin is located 42 miles eastof the power plant, and 8 miles south of the freeway.To connect power to the two towns, the power plant wantsto build one junction station along the freeway then runpower out to the two cities from the junction station. Thepicture below shows the general layout (not to scale), wherex is the length of power line run along the freeway (thelength from the power plant to the junction at point P). Yourboss has asked you to determine where the junction stationshould be built.Cortez49 miPmi8 mi42 miJoplinFind a formula for the length of power line needed to runfrom the junction at point P out to Cortez as a function of x.Length from P to Cortez = Find a formula for the length of power line needed to runfrom the junction at point P out to Joplin as a function of x.Length from P to Joplin :Submit QuestionFind a formula for total length of cable needed for runningall three length of cable.Total LengthSubmit QuestionUse your calculator to find the value of x that minimizes thetotal length of cable needed.The minimum occurs when xMake sure your answer is accurate to at least 2 decimalplaces.Submit QuestionWrite a letter to your boss at the power plant,recommending placement of the junction station. Make sureto convey your results in simple English. Include anyadditional considerations beyond cable length you think thecompany should consider.

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You are working for a power plant that is located on a highway that runs east to west. The town of Cortez is located 49 miles east of the power plant, and 6 miles north of the freeway. The town of Joplin is located 42 miles east of the power plant, and 8 miles south of the freeway. To connect power to the two towns, the power plant wants to build one junction station along the freeway then run power out to the two cities from the junction station. The picture below shows the general layout (not to scale), where x is the length of power line run along the freeway (the length from the power plant to the junction at point P). Your boss has asked you to determine where the junction station should be built. Cortez 49 mi P 6. mi 8 mi 42 mi

You are working for a power plant that is located on a highway that runs east to west. The town of Cortez is located 49 miles east of the power plant, and 6 miles north of the freeway. The town of Joplin is located 42 miles east of the power plant, and 8 miles south of the freeway. To connect power to the two towns, the power plant wants to build one junction station along the freeway then run power out to the two cities from the junction station. The picture below shows the general layout (not to scale), where x is the length of power line run along the freeway (the length from the power plant to the junction at point P). Your boss has asked you to determine where the junction station should be built. Cortez 49 mi P 6. mi 8 mi 42 mi

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

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You are working for a power plant that is located on a
highway that runs east to west. The town of Cortez is
located 49 miles east of the power plant, and 6 miles north
of the freeway. The town of Joplin is located 42 miles east
of the power plant, and 8 miles south of the freeway.
To connect power to the two towns, the power plant wants
to build one junction station along the freeway then run
power out to the two cities from the junction station. The
picture below shows the general layout (not to scale), where
x is the length of power line run along the freeway (the
length from the power plant to the junction at point P). Your
boss has asked you to determine where the junction station
should be built.
Cortez
49 mi
P
mi
8 mi
42 mi
Joplin
Find a formula for the length of power line needed to run
from the junction at point P out to Cortez as a function of x.
Length from P to Cortez =

Find a formula for the length of power line needed to run
from the junction at point P out to Joplin as a function of x.
Length from P to Joplin :
Submit Question
Find a formula for total length of cable needed for running
all three length of cable.
Total Length
Submit Question
Use your calculator to find the value of x that minimizes the
total length of cable needed.
The minimum occurs when x
Make sure your answer is accurate to at least 2 decimal
places.
Submit Question
Write a letter to your boss at the power plant,
recommending placement of the junction station. Make sure
to convey your results in simple English. Include any
additional considerations beyond cable length you think the
company should consider.

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